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Convex Bodies: The Brunn–Minkowski Theory, Second Edition by Rolf Schneider

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6

Valuations on convex bodies

Besides Minkowski additivity of mappings on the space of convex bodies, we have already met several examples of a different kind of additivity. A mapping from a family image of sets into some abelian group is called additive, or a valuation, if the sum of its values at KM and KM equals the sum of the values at K and M, whenever image On suitable domains, a valuation is also known as a finite measure. Valuations on image play an ...

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